Impact of changing concavity indices on channel steepness and divide migration metrics

The concavity index, urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0001, describes how quickly river channel gradient declines downstream. It is used in calculations of normalized channel steepness index, urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0002, a metric for comparing the relative steepness of channels with different drainage area. It is also used in calculating a transformed longitudinal coordinate, urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0003, which has been employed to search for migrating drainage divides. A urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0004 value of 0.45 is typically assumed in studies. Here we quantify the variability in urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0005 across multiple landscapes distributed across the globe. We describe the degree to which both the spatial distribution and magnitude of urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0006 and urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0007 can be distorted if urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0008 is assumed rather than constrained. Differences between constrained and assumed urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0009 of 0.1 or less are unlikely to affect the spatial distribution and relative magnitude of urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0010 values, but larger differences can change the spatial distribution of urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0011 and in extreme cases invert differences in relative steepness: relatively steep reaches can appear relatively gentle as quantified by urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0012.These inversions are function of the range of drainage area in the considered watersheds. We also demonstrate that the urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0013 coordinate, and therefore the detection of migrating drainage divides, is sensitive to varying values of urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0014. The median of most likely urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0015 across a wide range of mountainous and upland environments is 0.425. This wide range of variability suggests workers should not assume any value for urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0016, but should instead calculate a representative urn:x-wiley:21699003:media:jgrf21424:jgrf21424-math-0017 for the landscape of interest, and exclude basins for which this value is a poor fit.